Triple bar

"For the horse jump, see Oxer"

The triple bar, ≡, is a symbol used in formal logic. It has the appearance of a "=" sign with a third line.

Logically, it has a similar meaning to the if and only if coupler ⇔. However, in some texts ⇔ is used as a symbol in logic formulas, while ≡ is for reasoning about those formulas (as in metalogic).

In addition, it has the completely separate meaning of modular equivalence in number theory: we write $a\; equiv\; b\; pmod\; N$ if "N" divides "a" − "b".

This symbol is also used when it appears in an equation which is a definition of its left-hand side.

It is also used for "identical equality" of functions; one writes $f\; equiv\; g$ for two functions "f", "g" if we have $f(x)\; =\; g(x)$ for all "x".

It is Unicode character 8801. The HTML entity ≡ also corresponds to the triple bar.